You may use
additional sheets of paper to solve the following questions, but please report
your results and conclusions in the space provided.Whenever possible, show your work for
potential partial credit.NOTE:When performing numerical calculations, keep
at least 4 digits after a decimal.(I.e., do NOT round .2265 to .23 or .227)BUDGET YOUR TIME WISELY!

1.As a favor to the
Dean of Admissions, you are going to perform some statistical analysis,
including a hypothesis test that will test the research question:“Does the average HanoverCollege student experience a lower
GPA in college than they did in high school?”Describe, in great detail,
the step-by-step methodology that
you would use to set up, perform, and conclude this test.I am not interested in specific calculations,
do not make up data or an outcome, just tell the story from beginning to
end.(20 points)

2.Like most fall
semesters, I am currently teaching two sections of Principles of Microeconomics,
and, although they receive the same assignments and exams, I am concerned about
whether the performance differs between the two sections.The table below summarizes the mean class
grade, as a proportion of the total possible points, and the number of students
in each section.Set up, conduct, and
explain the results of a hypothesis test to help me address my concerns.(12 points)

Section A

Section B

n = 18 students

n = 16 students

Mean grade = .7987

Mean grade = .7956

3.As a consultant to
the airline industry, you are given an assignment to develop a simple linear
regression model between the number of customer complaints (per 100,000
passengers) and the percentage of flights that arrive on time.

a.Write the
theoretical simple linear regression equation for this model, being sure to
specify which variable should be the dependent variable.Explain why you chose this variable as the
dependent variable.What is the expected
sign of the slope coefficient?Explain
your reasoning.(8 points)

b.Least squares
estimation will produce the intercept and slope of the estimated regression
line.In addition to these estimates,
what other pieces of information would you find useful in completing your
assignment?What does this information
tell you and why is it useful?(10
points)

4.In order to
determine whether or not there is a difference between the hourly wages of two
companies, the following data have been accumulated.

Company 1

Company 2

Sample size = 80

Sample size = 60

Sample mean wage = $6.75

Sample mean wage = $6.25

Sample standard deviation = $1.00

Sample standard deviation = $0.95

Your nosy roommate comments that, since one wage is higher
than the other that the problem ends there.Explain to your roommate why it is not as simple as that.Then conduct an appropriate test to determine
whether there is any significant difference between the hourly wages of the two
companies.Explain the results to your
roommate.(15 points)

5.Supermarkets
frequently price products such as bread and milk to attract customers to the
store.A manager of a dairy that
supplies milk to a supermarket wanted to know how sales of milk are affected by
different prices.Consequently, she
recorded the weekly sales (Sales) of milk at one supermarket, the price of a
quart of her company’s brand (Own Price) and the price of a quart of her
competitor’s brand (Rival Price).

a.Prior to
conducting least-squares regression, which of these three economic variables
should be the dependent variable?Do you
expect a positive or negative sign on each independent variable?In responding to these questions, be sure to
use economic analysis to explain your reasoning.(9 points)

Using Excel, you produce the following table of
information.Use this output to answer
the questions below.Sales are measured
in number of quarts sold per week.Milk
prices are measured in cents per quart.

SUMMARY OUTPUT

Regression
Statistics

Multiple R

0.702328063

R Square

Adjusted R Square

0.472581635

Standard Error

558.6819057

Observations

52

ANOVA

df

SS

MS

F

Regression

2

14887582.57

7443791.287

23.84871

Residual

49

15294148.12

312125.4718

Total

51

Coefficients

Standard Error

t Stat

P-value

Intercept

857.5655311

4.336660978

7.19E-05

Own Price

-46.7736569

10.83136113

7.64E-05

Rival Price

58.52364212

10.46412923

9.86E-07

b.Begin by computing
and filling in any necessary omitted information.(5 points)

c.Carefully
interpret each estimated coefficient.Do
they make economic sense?Explain.(6 points)

d.What do the
results tell you with regards to the statistical significance of each
coefficient?Be thorough and include the
necessary hypothesis tests.(9 points)

e.Interpret and use
the appropriate measure to comment upon the ability of the estimated model to
fit the data.(6 points)